The primary purpose of this project is to determine whether multiple intramuscular injections of the APL 400-003 HIV DNA plasmid vaccine at dose levels of 30, 100, and 300 micrograms can be administered safely to asymptomatic HIV-infected patients. As a secondary objective, the protocol is designed to evaluate whether these multiple intramuscular injections of the APL 400-003 Vaccine might enhance existing antigen-specific immune responses, especially T cell responses, when administered to asymptomatic HIV-infected patients and to characterize the immune response profile of these patients pre- and post-injection, and to monitor indicators of progression of HIV infection in these asymptomatic HIV-infected patients.